Algorithm and Data Structure - Binary Search

Algorithm and
Data Structure
Andi Nurkholis, S.Kom, M.Kom
Study Program of Informatics
Faculty of Engineering and Computer Science
SY. 2020-2021
May 10, 2021

3
What is Searching?
Searching for data stored in different data structures
is a crucial part of pretty much every single
application.
There are many different algorithms available to
utilize when searching, and each have different
implementations and rely on different data
structures to get the job done.

4
Searching
Algorithm
1) Linear Search
2) Binary Search
Being able to choose a specific algorithm
for a given task is a key skill for
developers and can mean the difference
between a fast, reliable and stable
application and an application that
crumbles from a simple request.

6
Binary Search
Binary Search is a searching algorithm for finding an element's
position in a sorted array.
In this approach, the element is always searched in the middle of a
portion of an array.
Binary search can be implemented only on a sorted array of items.
If the elements are not sorted already, we need to sort them first.

Steps of Binary Search
1. Start with the middle element:
a. If the target value is equal to the middle element of
the array, then return the index of the middle
element.
b. If not, then compare the middle element with the
target value,
• If the target value is greater than the number in
the middle index, then pick the elements to the
right of the middle index, and start with Step 1.
• If the target value is less than the number in the
middle index, then pick the elements to the left of
the middle index, and start with Step 1.
7

Steps of Binary Search (cont.)
2. When a match is found, return the index of the element
matched.
3. If no match is found, then return -1
8

Example
9
data_1 = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21}
Find value 15 in array data_1
data_2 = {1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31}
data_3 = {1, 5, 9, 13, 17, 21, 25, 29, 33, 37}

Answer 1
10
Low
1 3 5 7 9 11 13 15 17 19 21
Value searched for 15
Value in middle-index array is 11
Is value 15 = 11?
FALSE
Is value 15 > 11?
TRUE
Then Algorithm is CONTINUE
If value searched greater than
value in middle-index array, then
searching continue to the right
High
Mid
Step 1

11
At each step, the middle-index changes
according to the direction of the search
At next step, low-index [1] changes to the
previous middle-index [11]. That is
because searching continues to the right
What is the meaning? The next high-index
[11] that changes will also cause the next
middle-index [15] to change

Answer 1 (cont.)
12
1 3 5 7 9 11 13 15 17 19 21
Step 2
Is value 15 = 15?
TRUE
Then Algorithm is STOP
Low High
Mid

13
Final Result
Value searched for 15 is FOUND
in step 2

Answer 2
14
Step 1
1 4 7 10 13 16 19 22 25 28 31
Is value 4 = 16?
FALSE
Is value 4 > 11?
FALSE
If value searched less than value in
middle-index array, then searching
continue to the left
Low High
Mid

15
because searching continues to the left

Answer 2 (cont.)
16
1 4 7 10 13 16 19 22 25 28 31
Step 2
Is value 4 = 7? FALSE
Is value 4 > 7? FALSE
Low High
Mid

17
previous middle-index [7]. That is because
searching continues to the left

Answer 2 (cont.)
18
1 4 7 10 13 16 19 22 25 28 31
Step 3
Is value 4 > 11? FALSE
Low High
Mid

19
Final Result
in step 3

Answer 3
20
Step 1
1 5 9 13 17 21 25 29 33 37
Is value 33 > 17? TRUE
For an even-number array, done
N/2, then N-1. For this case, 10/2
= 5, then 5-1 = 4. Therefore,
middle-index array is 4-index.
Low High
Mid

21

Answer 3 (cont.)
22
1 5 9 13 17 21 25 29 33 37
Step 2
Low High
Mid

23

Answer 3 (cont.)
24
1 5 9 13 17 21 25 29 33 37
Step 3
Low High
Mid

25

Answer 3 (cont.)
26
1 5 9 13 17 21 25 29 33 37
Step 4
Is value 33 = 33? TRUE
Low High
Mid

27
Final Result
in step 4

Advantage of Linear Search
1. It eliminates half of the list from further searching by using the
result of each comparison.
2. For large array of data, it works significantly better than linear
search.
28

Disadvantage of Linear Search
1. The algorithm requires the array to be sorted first
2. In implementing, the algorithm more difficult
than linear search
29

Thank You, Next …
Sorting
May 10, 2021
Andi Nurkholis, S.Kom, M.Kom
Study Program of Informatics
Faculty of Engineering and Computer Science
SY. 2020-2021

Algorithm and Data Structure - Binary Search

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